Combined EEG and immersive virtual reality unveil dopaminergic modulation of error monitoring in Parkinson’s Disease

Detecting errors in your own and others’ actions is associated with discrepancies between intended and expected outcomes. The processing of salient events is associated with dopamine release, the balance of which is altered in Parkinson’s disease (PD). Errors in observed actions trigger various electrocortical indices (e.g. mid-frontal theta, error-related delta, and error positivity [oPe]). However, the impact of dopamine depletion to observed errors in the same individual remains unclear. Healthy controls (HCs) and PD patients observed ecological reach-to-grasp-a-glass actions performed by a virtual arm from a first-person perspective. PD patients were tested under their dopaminergic medication (on-condition) and after dopaminergic withdrawal (off-condition). Analyses of oPe, delta, and theta-power increases indicate that while the formers were elicited after incorrect vs. correct actions in all groups, the latter were observed in on-condition but altered in off-condition PD. Therefore, different EEG error signatures may index the activity of distinct mechanisms, and error-related theta power is selectively modulated by dopamine depletion. Our findings may facilitate discovering dopamine-related biomarkers for error-monitoring dysfunctions that may have crucial theoretical and clinical implications.

Making an error triggers specific electroencephalogram (EEG) signatures such as mid-frontal theta increases, delta power increases, and error-related negativity and positivity [21][22][23][24] . While smaller in amplitude and higher in latency 25 , similar signatures are also triggered when observing action errors 26 . Specifically, observing errors by others causes increased mid-frontal theta and frontal error-related negativity (oERN) and positivity (oPe). These changes are seen when observing an error committed by another 27 , by a partner during motor interactions 28,29 , and by an embodied virtual arm observed from a first-person perspective 30,31 (1PP). The observation-related error-monitoring components show a smaller amplitude and delayed latency than the execution-related components 25 . Throughout this article, we will use Pe and ERN to indicate error-execution-related positivity and error-negativity findings, respectively, and oPe and oERN to indicate error-observation-related findings.
Increasing neuroanatomical and functional evidence suggests that the prefrontal cortex, including the dorsal anterior cingulate cortex (ACC), generates error-related mid-frontal theta and ERN as a low-level mismatch between actual and expected responses 22,[32][33][34][35] . Conversely, Pe's origin is less clear. It has been associated with the engagement of different areas, such as the anterior parts of the ACC 36 , posterior parts of the cingulate 37 and insular 38 cortices, which have also been associated with the salience network 8,39,40 . Pe/oPe appear to signal the awareness of an error following motivational and affective events and may be associated with post-error adaptation 41,42 .
The distinct cortical involvement of these error-related responses is consistent with evidence suggesting the existence of independent mechanisms underlying the error-monitoring system 43,44 that appear to rely on distinct neurotransmitters 36,45 . Overbeek, Nieuwenhuis & Ridderinkhof (2005) and other pharmacological studies 46 have shown that the mid-frontal cortex is densely targeted by ascending dopaminergic projections from the ventral tegmental area 47 (VTA). These might affect mid-frontal theta and ERN amplitude but not the Pe and error-related delta activity, which have been associated with locus coeruleusnorepinephrine system activity [48][49][50] .
The VTA's level of dopaminergic neuron degeneration might result in different disease progression severity and non-motor function alterations 51 . Indeed, studies investigating the effects of neurochemical lesions in the VTA, a major source of dopaminergic projections to the forebrain, in rats found a 30-46% reduction in dopamine that did not alter P3-like potentials in intracranial recordings 52,53 . Despite a few studies with similar findings, the evidence remains unclear since no study has investigated the dopaminergic influence on different error-monitoring processes. Therefore, testing PD patients under dopaminergic medication (on-condition) and after dopaminergic withdrawal (off-condition) could be an ideal model for exploring dopamine's selective influence on different EEG error-monitoring markers.
While a few EEG studies have reported reduced ERN and theta amplitude during action execution in PD patients, others reported mixed Pe and oPe results 8,9 . It should be noted that only two studies used the time-frequency (TF) approach 54,55 , and only one found no difference in conflict-related theta due to dopaminergic medication 55 . Therefore, it remains unclear whether dopamine balance is necessary for human mid-frontal theta activity during error monitoring.
In addition to theta, other frequencies are implicated in errormonitoring processes and PD. Delta (2-4 Hz) frequencies were associated with the Pe response, with erroneous actions characterised by a positive deflection in the time domain and an enhanced delta power 47,56 . However, several studies found beta alteration patterns in patients with dopaminergic deficiency 57 , including an exaggerated burst of beta oscillations, which has often been associated with motor impairments in this population.
Here, we investigated how dopamine balance influences errormonitoring mechanisms by recording EEGs in the same PD patients while on-and off-condition and in healthy controls. Participants were immersed in a virtual scenario and passively observed a virtual arm executing correct or incorrect actions from a 1PP. This approach proved adept at inducing the illusion of ownership over the virtual body, allowing us to investigate error processing in highly realistic circumstances 30,31,58 . Moreover, exploring action processing without overt movements allowed us to control any confounding due to interindividual differences in task difficulty or response speed that might occur between patients.
We hypothesised that distinct error processes co-exist 43 and that off-condition patients would show specific alterations in the electrocortical error processing markers purportedly modulated by dopamine (i.e. mid-frontal theta) without affecting markers that are less related to it (i.e. oPe and delta 56,59 ). Specifically, we expected off-condition PD patients to show a different thetaresponse (i.e. less theta activity in response to errors) than healthy controls (HCs), while the on-condition PD patients would have a similar activity to the HCs due to their dopaminergic treatment. We also explored whether the dopaminergic treatment produced a difference in theta activity between on-and off-conditions. We expected no difference in the oPe response among the three groups since this process appears not to be influenced by dopamine balance 59 . Furthermore, relationships between EEG motor error-observation markers and clinical scales assessing motor disability and disease progression were explored to highlight potential associations between clinical deficits and EEG states during different dopaminergic conditions. Previous studies have shown the relationship between frontocentral theta, executive functions, and working memory abilities 60,61 . In this study, we explored the relationship between differential theta activity and tests assessing executive functions in PD patients. Specifically, we used two tests previously used in error-monitoring studies in the neurological and psychiatric populations 62,63 . We expected relationships between differential theta activity and executive function' tests in PD since theta activity is a neural signature of cognitive control 4 . Furthermore, many studies have shown how PD patients without dopaminergic treatment tend to show exaggerated beta activity bursts during resting-state 64 and cognitive control tasks 65 . To date, no study has investigated beta-band activity during error observation in the context of dopaminergic treatment. However, since previous studies have shown that dopamine improves neural communication associated with beta-band activity 66 , we expected to observe beta frequency modulation only in off-condition PD patients compared to HCs since beta activity will be higher in PD patients without dopaminergic treatment 57 .

RESULTS
Clinical deficits relative to dopamine states inferred from UPDRS III and H&Y scales Consistent with the expected beneficial dopamine effect for extrapyramidal symptoms, the UPDRS III scores decreased significantly between off-condition (M = 37.21, SD = 10.04) and on-condition (M = 17.67, SD = 6.80) PD patients (t (13) = 5.39, p = 0.0001). H&Y scores ranged between 2 and 2.5 for on-and off-condition PD patients, except for one with a score of 3 in the off-condition. This finding suggests that all PD patients included in the study had bilateral disease since scores <1.5 indicate unilateral involvement only. Changes in H&Y scale values with different dopamine levels indicates a similar effect with significantly higher values in off-condition (M = 2.32, SD = 0.32) than on-condition (M = 2.08, SD = 0.18) PD patients (t (13) = 2.78, p = 0.016; Table 1b). One patient was excluded from this analysis because their offcondition evaluation was missing. No significant correlation was found between UPDRS, H&Y, and EEG signals (theta, oPe).
Correlations between theta activity and executive function abilities No significant correlation survived multiple comparison correction.

EEG Time-domain analysis
Cluster-based statistics. We found significant differences in the within-group analysis for all three groups but with different spatial distributions. A significant difference was found between correct Similarly, the cluster-based permutation revealed a difference between on-condition (p = 0.0020, range 380-1000 ms) and offcondition (p = 0.0079, range 300-634 ms) PD patients. Offcondition PD showed greater voltage in frontocentral rather than parietal electrodes after observing erroneous actions, with increased time-limited activity ( Fig. 1). Cluster comparisons between groups did not show significant differences in the 0-1000 ms window.
Single-electrode statistics. An oERN analysis was not performed as a clear peak was not found on visual inspection. One possible interpretation of this negative finding is provided in the Discussion. Traditional oPe analyses (400-800 ms) showed that all groups differed significantly between correct and incorrect actions (Fig. 2). ANOVA comparing HCs and on-condition PD showed a significant condition effect (F (27,1) = 8.77, p = 1.05 × 10 −6 ; η 2 p = 0.52), with generally greater oPe values in HCs than in oncondition PD patients, and significantly greater oPe for incorrect than correct actions (F (27,1) = 29.11, p = 0.0060; η 2 p = 0.25). There was also a significant condition vs electrode interaction (F (27,1) = 11.96, p = 0.0010; η 2 p = 0.31). Post hoc analyses with multiple testing corrections showed that incorrect actions caused increased FCz and Pz electrode activity compared to correct actions.
The within-group ANOVA comparing on-and off-condition PD showed a significant condition effect (F (14,1)  No group effect was identified in any analysis. The absence of a group effect but the presence of a condition effect in the differential wave analyses is consistent with the absence of inter-group differences in the cluster-based permutation analyses, suggesting that all three groups had a consistently greater amplitude in their oPe responses to incorrect than correct actions. Also, Bayesian paired sample t-tests between on-and off-condition PD showed moderate evidence favouring the null hypothesis (BF 10 = 0.26), while independent-sample t-tests between HCs and on-or off-condition PD showed anecdotal evidence supporting the null hypothesis (BF 10 = 0.41 and BF 10 = 0.39, respectively).

TF domain analysis
Theta (4-8.1 Hz) Cluster-based statistics: We found significant differences between incorrect and correct actions in the HCs (p = 0.0019, range 208-888 ms) and on-condition PD (p = 0.011, range 0-648 ms), with greater theta activity for incorrect actions and a most pronounced difference over the central areas. However, there was no significant difference between incorrect and correct The ANOVAs on the differentials showed no significant effects when comparing HCs and on-condition PD and on-and offcondition PD. However, there was a significant main group effect when comparing HCs and off-condition PD (F (27,1) = 6.31, p = 0.0182; η 2 p = 0.19). Post hoc analyses of this main group effect showed that off-condition PD had lower theta power in the differential activity (M DIFF = 1.59) than the HCs (M DIFF = 18.20; t (22.35) = 2.47, p = 0.021). Therefore, the increase in action errorrelated theta activity was lower in off-condition PD than in HCs.
The ANOVAs comparing the oPe (differential) and theta (differential) after z-score transformation on different electrodes (FCz/Pz) and response type (oPe/theta) showed no effects within or between groups. Similarly, to highlight potential differences between delta and theta-power activities, we also performed an ANOVA comparing theta (differential) and delta (differential) within each group and three ANOVAs between groups comparing both electrodes (FCz/Pz) and frequencies (delta/theta). The withingroup analyses showed a significant difference between differential delta and theta only in the off-condition PD for the main frequency factor (F (14,1) = 5.31, p = 0.0370; η 2 p = 0.28), with greater delta (M = 16.77) compared to theta (M = 1.59) power. No power difference between these frequencies was found between on-condition PD and HCs. The between-group analyses showed no significant differences in delta and theta activity.
The effect sizes (η 2 p) of differential theta activity show a large effect in the magnitude of between off-condition PD vs HCs (p = 0.0182; η 2 p = 0.19) and off-vs. on-condition PD (p = 0.1466; η 2 p = 0.14), while a small effect between on-condition PD vs HCs (p = 0.2544; η 2 p = 0.05). The effect sizes of the main response effect (oPe/theta) in the analysis that considered the differential of both oPe and theta after z-score transformation show a medium effect in the off-condition PD (p = 0.1895; η 2 p = 0.12), and a small effect in on-condition PD (p = 0.7726; η 2 p = 0.01) and HCs (p = 0.4213; η 2 p = 0.05). The effect sizes of the main frequency effect (delta/theta differential) show a large difference in magnitude in the off-condition PD (p = 0.0370; η 2 p = 0.28), while small effects have been found in the on-condition PD (p = 0.4459; η 2 p = 0.04) and HCs (p = 0.5100; η 2 p = 0.03).
Other EEG frequencies potentially involved in error monitoring Delta (2)(3)(4) Cluster-based statistics: We found significant differences within the HCs (p = 0.0080, range 0-1000 ms), on-condition PD (p = 0.0020, range 0-1000 ms), and off-condition PD (p = 0.0040, range 0-1000 ms) groups. In all three groups, clusters showed greater delta activity for incorrect than correct actions (Fig. 5). The difference was more prominent in the frontal and parietal areas in the HCs, but more prominent in the frontocentral areas in both groups of PD patients. There were no significant differences between groups when comparing the maps of incorrect and correct actions.
Cluster-based statistics: No significant alpha activity differences were associated with incorrect than correct actions in any group.

Beta (12.3-30.6 Hz)
Cluster-based statistics: Cluster-based permutation comparing incorrect and correct actions indicated a trend in the HCs (p = 0.0799, range 280-440 ms) with a central-contralateral distribution opposite to the observed arm (Fig. 5). On-condition PD showed no significant difference in condition. However, offcondition PD showed a significant difference (p = 0.0040, range 150-1000 ms), mainly in the central electrodes. The independentsample comparison between groups indicated a significant difference between the HCs and off-condition PD (p = 0.0359, range 678-968 ms), reflecting higher beta power in the central areas with off-condition PD than with HCs ( Fig. 5; see Discussion).
Subjective reports during the virtual reality-EEG task A lower sense of ownership was reported for incorrect than correct trials in all three groups (M ± SD; HC COR = 58.09 ± 24.02 and HC ERR = 57.22 ± 26.27; on-condition PD COR = 65.37 ± 28.41 and PD ERR = 63.77 ± 29.58; off-condition PD COR = 59.60 ± 28.84 and PD ERR = 58.75 ± 27.20). However, within-and betweengroup analyses showed no significant group or condition differences (all p > 0.05). In addition, no significant correlations were found. Overall, participants in the three groups responded correctly to the catch questions, confirming their engagement in the task and their understanding of the observed action (correct answers: HCs = 94%, on-condition PD = 97%, and off-condition PD = 93%).

DISCUSSION
To explore dopamine's influence on the electrocortical dynamics of error monitoring, we recorded EEG in patients with PD as they observed correct and incorrect actions performed by a virtual arm observed from a 1PP. We used a within-subject approach to test the same PD patients under dopaminergic medication (oncondition) and after dopaminergic withdrawal (off-condition). A control group of healthy participants was also included.
Our first observation was that theta power increased contingent upon observation of incorrect actions in HCs and on-condition PD patients but not in off-condition PD patients, indicating that dopamine depletion modifies this neurophysiological performance monitoring marker. Our second observation was that, unlike theta activity, oPe and delta power were higher for incorrect than correct actions in HCs and on-and off-condition PD patients, indicating that error monitoring comprises processes that may or may not be impacted by levels of dopamine balance. Furthermore, off-condition PD patients showed a stronger errorrelated beta response with incorrect than correct actions, also when comparing the differential activity of off-condition PD with HCs. No such effect was observed with on-condition PD patients.
In response to incorrect actions, off-condition PD patients showed abnormal theta-band activity with no power increase. Crucially, when the same PD patients were tested just after taking their regular dopaminergic medication (on-condition), theta activity in response to incorrect actions was restored, leading to the same pattern as HCs 22 . It should be noted that consistent with previous studies 63, 64 , we did not observe a difference in theta activity contingent upon error monitoring between on-and offcondition PD. The fact that PD patient responses did not differ between their on-and off-conditions might reflect different factors, including variability in individual responses to dopaminergic treatment 16 and dopaminergic neuron degeneration in their VTAs 67 . Importantly, a significant theta-power difference in response to incorrect actions was found between HCs and offcondition PD patients. Our off-condition PD patients had a longer withdrawal phase (~18 h) and increased extrapyramidal motor symptom severity (mean UPDRS = 37) from their dopaminergic medication compared to previous studies 11 . These factors might have allowed us to better highlight dopamine's contribution to performance monitoring compared to previous studies using a shorter withdrawal period that found no differences 36,64 . Tellingly, no differential error-related theta activity was found between HCs and on-condition PD patients. Also, despite not showing a significant difference between oPe and theta, off-condition PD qualitatively showed a medium effect size, that was greater than the two other groups. In addition, to highlight potential differences between error-monitoring processes, analyses on theta and delta differentials showed a significant difference and a large effect size in the response type in off-condition PD patients (i.e. an increased delta-but not theta-power); this effect was not shown by the other two groups. Delta and theta differential activities, differently than oPe (ERP) and theta (TF), may be more informative to compare as they both consider also EEG activity which is not time-and phase-locked with the event. This result further suggests dopamine's central role in performance monitoring related to mid-frontal theta and in regulating information precision during predictive processes triggered by salient and unexpected events 18 , as recently reported in the social context [68][69][70] . Previous studies suggested a link between frontoparietal theta activity and executive functions, such as working memory 71 and eye-blink decay 72 , which have been associated with executive dysfunction in PD. Others have found mixed effects such as beneficial or detrimental effects of the dopaminergic medication on the executive domain 73 . In this case, no significant correlation survived multiple comparison correction, suggesting a non-robust association between theta activity during error observation and behavioural indices of executive functions in the PD sample of this study.
Our results showed that observing incorrect actions produced detectable oPe in all groups. Both single-electrode and clusterbased permutation analyses showed that observing incorrect actions was characterised by increased ERP amplitude compared to observing correct actions. There was a topographical oPe centroparietal distribution and greater effects over the central (FCz) than the parietal (Pz) electrode. The spread of activity over the central rather than posterior electrodes is potentially consistent with studies showing that oPe is a cortical response characterised by subcomponents spreading over frontocentral and centroparietal electrodes 41,74 , that ageing and pathological populations often show component shifts from posterior to frontal areas, and that Pe/oPe are characterised by large topographical distribution variability across studies and clinical populations 41 .
While on-condition PD patients showed generally lower amplitude values than HCs, the differential waves (incorrect minus correct) showed no oPe response differences between groups. Notably, the non-significant difference in the oPe response between groups is consistent with the hypothesis that this component's generation is independent of the dopaminergic system 59 . This evidence is consistent with findings in other clinical populations, such as patients with ACC lesions 8,9,75 in which the Pe but not the ERN or theta was unaltered. Patients with lateral prefrontal lesions extending into the insula had reduced Pe responses 2,76 . This finding suggests that activities associated with Pe activity might engage a neural network involving the ACC and anterior insula and somatosensory areas 49 that might be spared in PD.
Surprisingly, we did not find any oERN, an error detection marker present in previous studies with young adults 30,31,58 . However, it should be noted that this component was absent in older populations investigated with a paradigm very similar to ours 77 . We speculate that its absence may reflect weak oERN modulation in aged individuals [78][79][80] . Another related explanation is that TF analyses might be more sensitive to phase-and nonphase-locked activity during continuous actions (e.g. theta), while ERPs are more sensitive to discrete events (e.g. ERN; 81,82 ). Indeed, previous data suggest that ERN is dominated by intermittent theta-band phase-locking 83 . However, observing an error also elicits non-phase-locked activity. Therefore, not all mid-frontal activity is associated with oERN generation 29,58 .
We also hypothesise that oERN's absence might not be related to the missing embodiment rating effects because participants in the three groups still reported a general feeling of ownership over the virtual arm, albeit with non-significant differences across conditions 58 . Moreover, even when an oERN was not identified, the typical theta power increase in response to incorrect actions was observed. It should be noted that drawing firm conclusions on this point is complicated by sample characteristics and task novelty compared to traditional experimental setups. Moreover, oERN's absence was somewhat unexpected. Future studies with ad hoc experimental designs are required on this important issue (e.g. investigating error responses across ages in different experimental setups).
Studies have shown that alpha 84 , delta 47,56 , and beta 85 frequencies may potentially be associated with error-monitoring processes. In this study, no error-related modulation was found for the alpha band. Instead, delta activity was higher for incorrect than correct actions in all groups. This finding is consistent with the belief that in a filtered signal, delta activity is associated with the Pe/oPe response in the time domain 47,56 . Interestingly, our results showed how this error-monitoring marker is not influenced by dopamine depletion. The enhancement in error-related delta activity and oPe in response to observing incorrect actions in HCs and on-and off-condition PD suggests that this mechanism is preserved in PD. Moreover, this finding contrasts with the absence of an error-related theta-response in off-condition PD patients, suggesting that dopaminergic projections may not have a prominent direct role in error-related delta and oPe generation.
Analysis of beta-band showed error-related increased in PD off, within-group and also when contrasted with HCs. Beta rhythm has been associated to sensorimotor control [86][87][88] , learning tasks 89 , and long-distance communication between visual and sensorimotor areas 90 . Previous studies on epileptic patients showed that alpha and beta frequency modulation was present while executing and observing reach and grasp actions 91 . Moreover, lower rhythms, such as delta and theta (<8 Hz), were more involved during movement execution than observation 92 . These results suggest that parallel neurophysiological processes (e.g. beta frequencies) can be observed during different movement modalities. Local subthalamic nucleus field recordings have associated excessive beta activity in PD patients with pathophysiological motor symptoms 93 that were restored by dopaminergic treatment 94,95 . Previous studies indicate that beta rebound was stronger after incorrect actions, suggesting beta's potential role in evaluating action significance and active response inhibition 85 . Off-condition PD patients showed a stronger error-related beta response in this study. However, no such effect was observed in on-condition PD patients in whom dopaminergic medication appears to suppress beta activity 94 . Therefore, while HCs showed greater theta than beta involvement in error responses, off-condition PD patients appear to show the opposite pattern. Future studies must investigate whether PD compensates for the involvement of mid-frontal theta with higher frequencies during dopaminergic withdrawal. It may be of particular interest to explore whether increased beta activity might be detrimental 57 or represent a compensatory mechanism rather than a pathophysiological marker 96 .
Concerning the relation between the UPDRS-H&Y and EEG signals, no significant correlation was found. Similar lack of correlation was found also in previous reports 55 , in which patients in on-condition had lower scores than off-condition in the UPDRS-III, but this result did not correlate with the EEG signal. Further, the scores obtained with the UPDRS III are related to patients 'motor ability' and it allows to evaluate the efficacy of the dopaminergic medication in improving general motor symptoms; however, this might be not directly related with the error-monitoring signals obtained within this task, in which a direct and active motor performance was not required.
Even when participants qualitatively reported a greater sense of ownership during the performance of a correct rather than incorrect action, analyses of the embodiment ratings did not show a significant difference between conditions. This result contrasts with previous studies on young adults 30,31,58 . While somewhat speculative, several explanations for between-study differences can be proposed. First, we tested old adults in this study, contrasting with our previous reports. Second, we asked participants to report embodiment over the artificial limb in 30% rather than 100% 30 of trials and only asked questions about feelings of ownership and not agency, which has also been associated with action monitoring [96][97][98] , to avoid long sessions and prevent patient fatigue. However, despite not showing a significant difference between incorrect and correct actions, our participants reported a general feeling of ownership that was >50% on the 0-100 VAS scale, consistent with previous reports on the feelings of embodying a virtual arm 31,58,99 . Therefore, we suggest that participants feel ownership of their virtual arm and that the process we are studying can be defined as monitoring actions performed by an embodied virtual arm.
Previous studies have highlighted the advantages of using a virtual task to induce the illusion of committing an error from a 1PP 30 . Here, correct and incorrect actions are performed by an arm calibrated to the participants' body size, something that would be impossible with traditional setups. Therefore, many recent studies have suggested that virtual reality could be a promising technique for cognitive and motor rehabilitation 100 . PD patients mostly answered the catch questions correctly. Indeed, we expected a high accuracy rate since the assignment was extremely easy and not performed under time-pressure conditions.
Our approach allowed us to directly investigate how distinct electrocortical signatures to errors are differently affected by dopamine balance in PD patients. This study's strengths include using an ecological and short (~20 min) immersive virtual reality task that tested the brain's reaction to errors in PD patients without confounding effects due to movement speed or difficulty 101 . Participants qualitatively reported a greater sense of ownership during correct rather than incorrect actions. However, while their scores were consistent with previous studies 30, 31 , statistical analyses did not show significant differences between conditions.
We acknowledge some potential limitations. First, PD patients were tested twice, while HCs were tested only once. However, consistent with previous studies 55 , we can reasonably exclude a learning or habituation effect because the adopted task involved simple action observations and did not require the acquisition of task-specific abilities. Moreover, reactivity to errors is due to their lower frequency, making them odd events. Crucially, we have already shown that electrocortical error detection and monitoring markers are found even when incorrect events comprise 70% of trials 30 . This finding suggests that the deviation from expected motor plan executions is perceived as a salient and significant event independent of its occurrence frequency 30 . Therefore, the brain's reaction to the observed motor errors found in this study cannot be ascribed to an oddball effect 79 . Second, we did not record the electromyography to monitor real movements during the experiment, although we asked participants to remain still and avoid movement. Third, the main analyses were performed using two electrodes (FCz and Pz) that were specified a priori based on previous studies. However, this could have hidden the signal's richness. To compensate we also provided all-brain electrode analyses but approaches other than cluster-based permutation to identify electrode clusters in a button-up manner could be relevant for investigating the involvement of single or multiple brain regions. In particular, studies with intracranial electrodes 102 may have allowed us to circunvent the electrode level limitations due to volume conduction issues and identify cortical regions involved in specific monitoring processes.
Finally, other neurotransmitters might play a role in performance monitoring through direct ACC modulation or their influence on the dopamine system 55,103 . Future studies should explore the role of neurotransmitters, such as serotonin, norepinephrine, gamma-aminobutyric acid (GABA), and adenosine in cooperation with dopamine in orchestrating error processes 33 in cohorts with different phenotypes 104 .
In conclusion, this study expanded research on the complex architecture of the monitoring system in older adults and neurological populations by providing support for the hypothesis that error-related theta activity is influenced by dopamine balance 44,48,105 . Error-related theta activity modulation contingent upon dopamine depletion found in this study may provide a foundation for future studies on neurophysiological biomarkers related to prediction processing and model updating 38,106,107 that may ultimately help to understand error monitoring during action observation in PD patients.

METHODS Participants
Seventeen patients with PD participated in this study. The MorePower (version 6.0.4 108 ) software was used to compute the sample size. It indicated that 14 participants would be sufficient to provide 85% power with an alpha of 0.05 and a partial η 2 of 0.4 based on a previous study using the same paradigm to assess the electroencephalographic error-monitoring markers 58 . All participants had normal or corrected-to-normal visual acuity. The inclusion criteria were: (i) idiopathic PD diagnosis according to the United Kingdom PD Society brain bank criteria on the unified PD rating scale (UPDRS 109 ); (ii) a mini-mental state examination (MMSE) score >26 110 ; (iii) the absence of other neurological and psychiatric diseases; (iv) treatment with daily doses of dopamine or dopamine agonists (equivalent levodopa doses; see Table 2 for more details). One patient was excluded due to possible incorrect medication and a lack of motor scale data. One patient withdrew from the study. Therefore, our final group of 15 PD patients   comprised five females and ten males aged (mean [M] ± standard deviation [SD]) 70 ± 9 with 12 ± 4 years of education. Sixteen healthy participants served as HCs. One HC was excluded due to impaired vision, and one due to MMSE below cut-off. Therefore, our final group comprised 14 HCs matched for age and education with the PD patients: five females and nine males aged 70 ± 6 with 13 ± 3 years of education. HCs were included according to the following criteria: (i) absence of neurological or psychiatric diseases in anamnesis; (ii) absence of subjective cognitive disorders; (iii) absence of medications with psychotropic action; (iv) MMSE score >26 110 (see Table 1a for details).
PD patients received an extensive neuropsychological assessment during their on-condition (under treatment), as part of a specialised hospital clinical practice. Demographic and clinicals information of PD patients and main neuropsychological tests that have been considered of interest for the current study are shown in Table 2.
All participants were naïve to the purposes of this study and provided written informed consent. The experimental protocol was approved by the local Ethics Committee at the IRCCS Santa Lucia Foundation of Rome (reference number: CE/PROG.533) and performed according to the ethical standards in the 2013 Declaration of Helsinki.

Apparatus and stimuli
Participants sat in a Cave Automatic Virtual Environment (CAVE) with projectors directed to four walls of a room-sized cube (3 × 3 × 2.5 m 111 ). The virtual scenario consisted of a basic room with a Table (1:1 scale). A dark yellow parallelepipedon was located in the centre of the table with a blue glass on top of it. The virtual glass was placed in the participant's peripersonal space at a distance of~50 cm. Participants observed a virtual right arm projected outside their right shoulder and congruent in dimension and shape with their body from a 1PP (see Fig. 6, panel A). The virtual arm and the scenarios were created using Autodesk Maya 2015 and 3DS Max 2015, respectively. The kinematics of the avatar were realised in 3DS Max and implemented in the virtual scenario as an animated 3D mesh. The virtual reality-EEG experiment used a 3D immersive virtual environment rendered in CAVE using XVR 2.1 112 . Participants observed the virtual environment displayed through Optoma 3D active glasses. Their head position was tracked in real-time by an Optitrack System comprising eight infrared cameras placed inside the CAVE.

Experimental procedure
Patients were tested using different sessions on separate days. First, an extensive neuropsychological assessment was made while patients were under their dopaminergic treatment to ascertain their cognitive profile as part of standard clinical practice. For the experimental virtual reality-EEG task, the patients visited the laboratory in two separate sessions 15 days apart. In one session, they were examined within 60 min of their first medication intake (on-condition). In the other, they were examined after an 18 h washout from their dopaminergic medications used to treat PD (off-condition 113 ). The order of onoff-condition examinations was balanced across participants.
Before the virtual reality-EEG experiment began, participants underwent a calibration phase where the size and the position of the virtual right arm were adapted to their real arm. A short resting-state period was included before the experiment, which was not of interest to this study. Next, they performed a brief practice session (eight trials, four correct, and four erroneous) in which they familiarised themselves with the virtual arm's movements and the task. Each participant was requested to passively observe the virtual arm's movements (avoiding any movements of their real arm) and was informed that the goal of the movements was to reach and grasp the glass on the table. They were also informed that the action might or might not be successful.
The virtual reality-EEG task consisted of 110 trials per participant (70 correct and 40 incorrect virtual arm movements) with a total duration of~20 min. Including a smaller proportion of erroneous to correct actions was consistent with previous studies in which errors are often a salient infrequent event 47 . Previous studies using the current paradigm have used 30%:70% incorrect-correct actions 30,31 and their inversion (70%:30% 58 ). In this study, the choice to include a smaller number of erroneous (36%) to correct (64%) actions was preferred to maintain the infrequency of errors and provide a sufficient number of trials in this clinically aged population.
At the onset of each trial, a sound signalled the beginning of the action. During the trial, participants passively observed the Fig. 6 Schematic representation of the experimental paradigm and setup. A Images (c) and (d) show the participant immersed in a virtual scenario in the CAVE system while observing the real-size virtual arm from a 1PP during a correct (a) or erroneous (b) grasping action. B The timeline of a single trial. The avatar's action lasted~1000 ms, with the reaching phase equal for both outcomes. The onset of the avatar's armpath deviation is at 0 ms, and the end of the avatar's action occurs at 300 ms. The time windows for event-related potential (ERPs) and timefrequency (TF) analyses have been chosen a priori based on previous studies 30,58 . movement of the virtual right arm from a 1PP. The total duration of the movement was 1000 ms. The movement's kinematics were identical for 70% of the action duration in both correct and incorrect conditions but could diverge in the final 30% leading to either a successful or unsuccessful grasping; 30,31,58,77 here a short videoclip of the paradigm: https://osf.io/rxeha). The deviation from the to-be-grasped object was identical in all erroneous trials (Fig.  6, panel B). The sequence of correct and incorrect trials was pseudorandomised. After the end of the action, the avatar's arm remained still for 1000 ± 50 ms before the screen went black.
During the inter-trial interval (ITI), one of three events occurred: (i) participants had to answer a catch question 'did the arm grasp the glass?' (yes/no) to confirm their engagement in the virtual reality-EEG task in 10 out of the 110 trials (4 incorrect and 6 correct); (ii) an empty black screen was presented in 65 out of the 110 trials; (iii) participants had to rate their illusory sense of embodiment over the virtual arm in 35 out of the 110 trials (13 incorrect and 22 correct). The illusion was verbally rated on a visual analogue scale (VAS) between 0 and 100 by answering the question, 'to what extent did you feel the virtual arm was yours?' (0 = no ownership, 100 = maximal ownership [114][115][116][117][118] ). In the first and third event types, the black screen lasted until a vocal response was given. In the second event, the experimenter pressed a key to start the next trial, producing a variable ITI (M duration =~4.000 ms).
After each EEG session, an expert neurologist administered the UPDRS-III to PD patients 109 -a 27-item scale in which each item is evaluated on a 5-point Likert scale (from 0 to 4), where the maximum total score of 108 reflects the highest disability leveland the Hoehn and Yahr scale 119 . These scales estimate the patients' motor performance and disease progress, respectively, and allowed us to evaluate the efficacy of dopaminergic medication in improving motor symptoms. Higher scores indicated higher disease severity, with levels <2 on the UPDRS-III found in healthy elderly 120 . The two scales were administered under both on-and off-condition PD patients.
EEG recording and processing EEG signals were recorded using a Neuroscan SynAmps RT amplifier system and 62 scalp electrodes embedded in a fabric cap (Electro-Cap International), arranged according to the international 10-10 system. Horizontal electrooculogram was recorded bipolarly from electrodes placed on the outer canthi of each eye. Online EEG signals were recorded continuously in alternating current mode with a bandpass filter (0.05-200 Hz) and a sampling rate of 1000 Hz. Impedances were kept below 5 kΩ. All electrodes were physically referenced to an electrode placed on the right earlobe and re-referenced offline to the common average across all electrodes. Offline, raw data were bandpass filtered with a 0.1-100 Hz filter (finite impulse response filter, transition at 40-42 Hz, and stopband attenuation at 60 dB). Independent component analyses (ICA 121 ) were performed on the continuous EEG signal, and components that were clearly related to blinks and ocular artefacts were removed (5.8 ICA components on average).
Event-related potential (ERP) analyses used an additional bandpass filter (0.3-30 Hz) applied to the continuous raw signal. The EEG signal was then downsampled to 500 Hz and epoched in wide windows 3 s in length, from −1.5 to +1.5 s, to avoid edge artefacts induced by the wavelet convolution in the TF analysis. Epochs were time-locked (0 ms) at the avatar's arm-path deviation, with direct current offset correction to the previous 300 ms preceding the deviation 29,58 . Each epoch was then visually inspected to remove residual artefacts (e.g. eye blinks) by checking for epochs exceeding ±100 µV amplitude 122 . After this procedure, a small proportion of trials were removed from the original datasets (HCs: 4.5%; on-condition PD: 1%; off-condition PD: 4%). Therefore, each group had a sufficient and comparable number of trials for correct (COR) and incorrect (INC) actions (M ± SD; HC TOTAL : 105 ± 5, HC COR = 67 ± 3, and HC INC = 38 ± 2; oncondition PD-ON TOTAL : 109 ± 3, PD ON COR = 69 ± 4, and PD ON INC = 39 ± 1; off-condition PD-OFF TOTAL : 106 ± 5, PD OFF COR = 67 ± 3, and PD OFF INC = 39 ± 2 123 ).
Unless otherwise specified, data were normally distributed (Shapiro-Wilk test), and parametric analyses were used. EEG analyses were performed using the Brainstorm toolbox (https:// neuroimage.usc.edu/brainstorm/ 124 ) and custom Matlab routines. Statistical analyses were performed using R software 125 . Effect sizes were calculated using Cohen's d. ERPs and TF statistical analyses were performed using the erpR R package 126 . Analyses excluded practice trials.

EEG analyses
Time-domain analysis. All ERP analyses were based on mean amplitude, as recommended by Luck and colleagues 127 . We analysed ERPs at a whole brain level using a time-point clusterbased permutation analysis with 1000 repetitions (using p < 0.05 to identify significant cluster differences), Monte-Carlo correction in the 0-1000 ms time window on all electrodes, and cluster comparisons within and between groups to assess neural pattern reliability and robustness over neighbouring data points 128,129 . In addition, analyses using all electrodes were used to capture potential data-driven modulations at the all-electrode level, which can be relevant in ageing and clinical populations where shifts in neural activation might be observed 130 . Moreover, traditional ERP analyses were performed. We did not analyse oERN since it was not observed during visual inspection of the time series in the a priori selected time window (see Discussion). The oPe is a P300like component maximally peaking at electrode Pz distributed on the frontal electrodes (e.g. FCz 41 ).
Separate analyses of variance (ANOVAs) were computed on a priori established time windows of interest (400-800 ms) to be consistent with previous studies 30,31 . Since PD patients have been tested twice (within factor) and HCs have been tested only once, three separate ANOVAs were computed: HCs vs on-condition PD including two within-subject factors (condition: inc or cor; electrode: FCz or Pz) and one between-subject factor (group: HCs or on-condition PD); on-vs off-condition PD including three within-subject factors (condition: inc or cor; group: on or off; electrode: FCz or Pz); HCs vs off-condition PD including two within-subject factors (condition: inc or cor; electrode: FCz or Pz) and one between-subject factor (group: HCs or off-condition PD). Comparisons with significant effects were subject to post hoc analyses with false discovery rate (FDR) corrections for multiple testing.
In addition, following golden-standard recommendations 127,131 , the ERP differential obtained by subtracting the correct from the erroneous condition was compared using three ANOVAs: on-vs off-condition PD, HCs vs on-condition PD, and HCs vs off-condition PD including two factors (group: HCs, on-condition PD, or offcondition PD; electrode: FCz or Pz). Comparisons with significant effects were subjected to post hoc analyses with FDR correction for multiple testing.
We also directly compared the z-transformed values of the oPe and theta power's differential activities to identify potential differences among the three groups, although these indices are obtained with different mathematical transformations and indices from the TF domain include also non-time and phase-locked activity. To this aim three ANOVAs considering electrode (FCz and Pz) and response (oPe and theta) were performed as well as three ANOVAs between groups; we could not perform one unique ANOVA in order to respect the dependency among the observations (i.e. PD are the same individuals). However, significance testing only allows rejecting the null hypothesis; it does not disentangle whether the null hypothesis should be accepted, or the lack of effect is due to inconclusive data 132 . Therefore, we examined evidence favouring the null within (onand off-condition PD) and between (on-and off-condition PD vs HCs) group effects on oPe. We performed a Bayesian paired sample t-test comparing oPe's differential index (incorrect minus correct) between on-and off-condition PD groups. We also performed two separate Bayesian independent-sample t-tests comparing oPe's differential index between HCs and on-or offcondition PD. This approach enabled us to determine whether the absence of a significant group effect could be interpreted as evidence favouring the null effect of the group on oPe.
TF domain analysis. We used a complex Morlet transformation to compute TF decomposition in the TF analysis. A mother wavelet with a central frequency of 1 Hz and time resolution of 3 s (full width half maximum) was designed in the Brainstorm software 124 . The other wavelets were computed from this mother wavelet and ranged from 1 to 80 Hz in 0.5 Hz logarithmic frequency steps. We separately normalised each signal and frequency bin relative to the baseline by computing the relative power change (%) over the TF decomposition as ERSP(f,t) = S(f,t) − S base /S base , where S(t, f) is the signal spectrum in a specific interval of time (t) and frequency (f), and S base represents the reference signal's mean power in the baseline interval (event-related spectral perturbation [ERSP]). To avoid edge effects, the power activity from −700 to −500 msthe window in which the avatar's movement was identical in erroneous and correct conditions-was used as the baseline interval (S base ). Positive and negative values indicate a decrease or increase in synchrony of the recorded neuronal population, respectively 87 , relative to a given reference interval when equal neural activity is expected. Here, a relative power increase or decrease represents a power modulation compared to the mean power activity at baseline.
We investigated the effect on the whole brain using time-point cluster-based permutation analyses with 1000 repetitions for each run (p < 0.05) and Monte-Carlo correction on a wide time window of 0-1000 ms to visualise the distribution on the scalp 55,134 . Cluster comparisons within and between groups were performed. In addition, consistent with previous studies [29][30][31]58 , the main theta activity analyses were computed focusing on the theta band (4-8.1 Hz) in the preselected time interval (300-700 ms) corresponding to 400 ms from the end of avatar's action.
Besides frontal regions, the brain's posterior regions were engaged in observational tasks involving passive observation of reaching movements 135 . In addition, an occipitotemporal theta-band increase was observed during the processing of body-part stimuli 29,136 . Similar to the ERP analyses, the theta analyses involved three separate ANOVAs among groups: one comparing HCs to on-condition PD 'including two withinsubject factors (condition: inc or cor; electrode: FCz or Pz) and one between-subject factor (group: HCs or on-condition PD); one comparing on-and off-condition PD including three within-subject factors (condition: inc or cor; group: on or off; electrode: FCz or Pz); and one comparing HCs and off-condition PD including two within-subject factors (condition: inc or cor; electrode: FCz or Pz) and one between-subject factor (group: HCs or off-condition PD).
Next, similar to the ERP analyses, the theta band's differential index (incorrect minus correct 137 ;) was compared. Comparisons with significant effects were subject to post hoc analyses with FDR correction for multiple testing. Besides theta (4-8.1 Hz), cluster-level analyses were performed on potential frequencies interest for error-monitoring processes in PD: 56,57,85 delta (2-4 Hz), alpha (8.1-12.3 Hz), and beta (12.3-30.6 Hz). We were particularly interested in potential differences between delta and theta-power activities since they have been previously associated with distinct error-monitoring processes 56,138 in the TF spectrum. Therefore, we also performed an ANOVA comparing theta (differential) and delta (differential) in each group and three ANOVAs comparing groups separately for both electrodes (FCz and Pz) and frequencies (delta and theta).

Clinical and neuropsychological testing
Clinical data on motor ability relative to dopaminergic medication were analysed. We performed two ANOVAs with dopaminergic medication as a factor (on or off) separately for the UPDRS III and H&Y scales. Correlations between them and EEG signals were performed to investigate clinical deficits relative to EEG states during different dopaminergic conditions. Neuropsychological tests assessing executive functions and cognitive control were also taken into consideration in on-condition PD patients since previous data suggested a relationship between theta and ERN activity and performance in tasks underlying executive functions 32,60,71 . These included the trail-making test (TMT, parts B and BA 139 ) and the Wisconsin card sorting test 62,63 . To assess the general cognitive functioning also the Mini Mental State Examination (MMSE 140 ) and Mini Mental Parkinson State Examination (MMPSE 141 ) were administered. We performed correlations between all-brain cluster-based permutation across time (0-1000 ms) in theta activity and the executive functions tests, with Montecarlo correction for multiple comparison, to observe the scalp distribution across electrodes. We also corrected the correlations for multiple comparison with false discovery rate (FDR) correction. In order to explore the link between clinical scales measuring patient's motor disability and EEG states during motor action observation, we correlated the UPDRS and H&Y scales as measured in "on" and "off" and the EEG correlates (oPe, theta).
Subjective reports during the virtual reality-EEG task Embodiment ratings and the catch answers were calculated for correct and erroneous actions in the three groups as previously described 31,58 . The embodiment question, 'How much did you feel that the arm was yours' (on a 0-100 scale), was present only in a subset of trials (12% of incorrect and 20% of correct trials). Mean embodiment ratings for each trial type were calculated for each participant. The scores were compared with three separate ANOVA, including condition (correct or incorrect) as a factor, compared HCs to on-or off-condiction PD and on-and offcondition PD. We explored associations between the sense of embodiment and electrocortical error processing indices using Spearman's rank correlations between embodiment ratings and theta error signatures. Each group's percentage accuracy was calculated for the catch trials.
Statistical analyses of clinical-neuropsychological data and subjective reports were performed using the R software 125 . We applied the Greenhouse-Geisser non-sphericity correction and Bonferroni multiple testing correction when appropriate.

DATA AVAILABILITY
The data are available in the Open Science Framework repository https://osf.io/z9rbu/.